Bipolars are slim DIP chips, same width as TTL chips. Their benefit is they are very high speed but they have very low capacity compared to normal eproms, often only used for lookup tables, often in the colour section of boards.
When people talk about PROMs they usually mean Bipolar PROMs, even tho a PROM technically is an OTPROM as it is programable but not erasable. The "one time" prefix is fairly superfluous if erasing is not an option.
The OTPROM (one time programable ROM) is the same chip internally as a normal EPROM, without the window. The window was actually a fairly expensive part of the chip so ditching that made things much cheaper. If you could somehow drill a hole in the top of the chip without wrecking the inards you could in erase it and re-use it.
What is the point of all these types? EPROM, OTPROM, Mask ROM?
Money basically, specifically saving it!
On boards the executable code is usually contained in EPROMs so if there were any bugs they could erase the chips and program with the new code without throwing any expensive parts in the bin. The price of EPROMs when these boards were made was very high, easily 25% of the price of the entire board. Once they were sure the game code was not going to change then they could save money by using OTPROMs in place of the EPROMs. Its very common to see boards with a mix of EPROMs and OTPROMs and there is a high chance that it is the EPROMs that contain the actual program code.
Mask ROMs are chips that are fabricated with the data built into the structure of the chip, these were commonly used from the very late 80s onwards for graphics and sound sample data - data they knew was 100% from day one and was never going to change.
On earlier boards you often see a mix of EPROMS and OTPROMs instead of the masks, the reasoning is the same - gfx and audio data that they knew was 100% correct so there was no need to spend money on chips that could be erased.
Mask ROMs solve the same problem but there was scope to save even more money. Of course setting up the manufacture of mask ROMs was expensive but if they were going to make enough the cost per unit would fall below that of using EPROMs or PROMs, especially for the very high capacity chips when the price of multi megabyte chips was over $100. An added bonus was that they could design whatever pinout they wanted. If the board was never going to use the /CE pin then that could be done away with, no need for a pin to take a programming voltage as the chip is never programmed, so that pin can go too. The result was they could have a chip with fewer legs and still have the same capacity, this is why some mask ROMs do not have a direct drop in EPROM equivalent. If you can shave a inch off the PCB size by having smaller chips then that in itself makes for a massive saving in manufacturing cost is you are making thousands of boards.
Of course once the masks were made any mistakes in the data were locked in and aside from throwing them away and making new ones they had no option but to live with it. I imagine the lead artist on Shadow Warriors got a roasting when it was discovered that the main characters socks changed colour between when he was walking or fighting. If that data was in mask ROMs then it would have cost hundreds of thousands of dollars to fix, which is probably why the "bug" is there to this day.
There is also the EEPROM - the electrically erasable programable ROM which doesnt need to be erased with UV light. Not seen much on arcade boards tho.